Queueing Theory

Bocharov, P. P.; D'Apice, C.; Pechinkin, A. V.

doi:10.1515/9783110936025

Cited by 74 publications

(59 citation statements)

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“…This model is widely used in applications of queuing theory (see, e.g. Bocharov, 2003), and many other areas in operations research and statistics. Harris (1968), however, has found that in practice the average waiting time may be affected by a number of factors, and it varies as a gamma variate.…”

Section: General-purpose Models For Waiting Timementioning

confidence: 99%

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A model of pedestrians’ intended waiting times for street crossings at signalized intersections

2013

Transportation Research Part B: Methodological

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For the purposes of both traffic-light control and the design of roadway layouts, it is important to understand pedestrian street-crossing behavior because it is not only crucial for improving pedestrian safety but also helps to optimize vehicle flow. This paper explores the mechanism of pedestrian street crossings during the red-man phase of traffic light signals and proposes a model for pedestrians' waiting times at signalized intersections. We start from a simplified scenario for a particular pedestrian under specific traffic conditions. Then we take into account the interaction between vehicles and pedestrians via statistical unconditioning. We show that this in general leads to a U-shaped distribution of the pedestrians' intended waiting time. This U-shaped distribution characterizes the nature of pedestrian street-crossing behavior, showing that in general there are a large proportion of pedestrians who cross the street immediately after arriving at the crossing point, and a large proportion of pedestrians who are willing to wait for the entire red-man phase. The U-shaped distribution is shown to reduce to a J-shaped or Lshaped distribution for certain traffic scenarios. The proposed statistical model was applied to analyze real field data.

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Section: General-purpose Models For Waiting Timementioning

confidence: 99%

“…Currently, the commonly used model of waiting time in queueing theory is the general-purpose exponential distribution (see, e.g. Bocharov et al, 2003). In traffic studies, the exponential distribution was also used to model pedestrians' waiting times for street crossings (e.g.…”

Section: Introductionmentioning

confidence: 99%

A model of pedestrians’ intended waiting times for street crossings at signalized intersections

2013

Transportation Research Part B: Methodological

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“…, 10, for the system without AQM-type dropping. For the M/D/2-type system with an infinite waiting room and without packet dropping, stationary probabilities p k can be derived by using the following algorithm (Bocharov et al, 2004):…”

Section: Numerical Resultsmentioning

confidence: 99%

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Tikhonenko

Kempa

2016

International Journal of Applied Mathematics and Computer Science

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A queueing system of the M/G/n-type, n ≥ 1, with a bounded total volume is considered. It is assumed that the volumes of the arriving packets are generally distributed random variables. Moreover, the AQM-type mechanism is used to control the actual buffer state: each of the arriving packets is dropped with a probability depending on its volume and the occupied volume of the system at the pre-arrival epoch. The explicit formulae for the stationary queue-size distribution and the loss probability are found. Numerical examples illustrating theoretical formulae are given as well.

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“…The equilibrium equation set (53) is of a peculiar feature, so we can use the technique based on the exclusion of certain states of the Markov chain and the bonding of the remaining subsets (Bocharov et al, 2004) for its solving.…”

Section: 1mentioning

confidence: 99%

Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Gaidamaka

Pechinkin

Razumchik

et al. 2014

International Journal of Applied Mathematics and Computer Science

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Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system M [X] |G|1 L, H | H, R with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system's mode are considered. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are given.

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Queueing Theory

Cited by 74 publications

References 0 publications

A model of pedestrians’ intended waiting times for street crossings at signalized intersections

A model of pedestrians’ intended waiting times for street crossings at signalized intersections

Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping

Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

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